I have already set it to "No notifications".
Yet, I still receive a brief email from postmaster stating
"Your Mailbox has exceeded its quota and a message from [SMTP:xxx@xxx.com] was rejected. Please clean your mailbox and ask the user to re-send."

Actually looking at this further, usage notifications should be per mailbox, not just postoffice. The mailbox usage notifications should be based on a designated percentage of assigned Mailbox Quota. When the percentage is reached it should have the options to notify the mailbox, the postmaster of the postoffice, or system admin.